Let $\displaystyle F (x, y, z) = 6yx^2$i+ $\displaystyle 2x^3$j+ $\displaystyle 6xy$k, and $\displaystyle C$ be the curve of intersection of the hyperbolic paraboloid $\displaystyle z = y^2 - x^2$ and the cylinder $\displaystyle x^2 + y^2 = 25$ oriented counterclockwise as viewed from above.

(i) Obtain a parametrization of the curve $\displaystyle C$ and use the result to evaluate $\displaystyle \int_{C} F \cdot d$r.

(ii) use Stokes's Theorem to evaluate $\displaystyle \int_{C} F \cdot d$r.